### Abstract

Effective bending moduli of a fluid membrane are investigated by means of the transfer-matrix method developed in our preceding paper. This method allows us to survey various statistical measures for the partition sum. The role of the statistical measures is arousing much attention, since Pinnow and Helfrich claimed that under a suitable statistical measure, that is, the local mean curvature, the fluid membranes are stiffened, rather than softened, by thermal undulations. In this paper, we propose an efficient method to observe the effective bending moduli directly: We subjected a fluid membrane to a curved reference plane, and from the free-energy cost due to the reference-plane deformations, we read off the effective bending moduli. Accepting the mean-curvature measure, we found that the effective bending rigidity gains even in the case of very flexible membrane (small bare rigidity); it has been rather controversial that for such a nonperturbative regime, the analytical prediction does apply. We also incorporate the Gaussian-curvature modulus and calculated its effective rigidity. Thereby, we found that the effective Gaussian-curvature modulus stays almost scale invariant. All these features are contrasted with the results under the normal-displacement measure.

Original language | English |
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Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 68 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2003 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics